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COMBINATORICS
2006
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13 years 4 months ago
Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness
Abstract. The geometric thickness of a graph G is the minimum integer k such that there is a straight line drawing of G with its edge set partitioned into k plane subgraphs. Eppste...
János Barát, Jirí Matousek, D...
CCCG
2009
13 years 6 months ago
On Graph Thickness, Geometric Thickness, and Separator Theorems
We investigate the relationship between geometric thickness and the thickness, outerthickness, and arboricity of graphs. In particular, we prove that all graphs with arboricity tw...
Christian A. Duncan
GD
1998
Springer
13 years 9 months ago
Geometric Thickness of Complete Graphs
We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straightline edges and assign each edge to a lay...
Michael B. Dillencourt, David Eppstein, Daniel S. ...
COMPGEOM
2004
ACM
13 years 10 months ago
The geometric thickness of low degree graphs
We prove that the geometric thickness of graphs whose maximum degree is no more than four is two. In our proofs, we present a space and time efficient embedding technique for gra...
Christian A. Duncan, David Eppstein, Stephen G. Ko...
GD
2005
Springer
13 years 10 months ago
Graph Treewidth and Geometric Thickness Parameters
Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph...
Vida Dujmovic, David R. Wood